Non-periodicity in chemostat equations: a multi-dimensional negative Bendixson-Dulac criterion.
We establish conditions which exclude periodic solutions in a simple chemostat with a single nutrient and N competing species. Growth rates are not required to be proportional to food uptake. Instead of a Lyapunov function approach, we develop and apply a multi-dimensional Bendixson-Dulac type exclusion principle based on differential forms.
Fiedler
Bernold
B
Institut für Mathematik, Freie Universität Berlin, Berlin, Germany. fiedler@math.fu-berlin.de
Hsu
Sze-Bi
SB
D000465:Algorithms; D019149:Bioreactors; D017753:Ecosystem; D053476:Extinction, Biological; D008954:Models, Biological; D010507:Periodicity; D011157:Population Dynamics